Paper XXII: Inflation from Topological Phase Transitions in the Hopf Vacuum

We propose that cosmic inflation arises within the topological soliton framework as a phase transition from the disordered (⟨ H⟩ = 0) Hopf vacuum to the ordered soliton–antisoliton condensate. The inflaton is identified with the Hopf-invariant density — the transition order parameter — requiring no scalar field beyond the Faddeev-Niemi field. The effective potential V(ψ) = V₀ (1 - e^(-√2/3 ψ/M_P))²β is derived from three ingredients: the O(3) Heisenberg universality class fixes the plateau and the exponent 2β = 0.732, the multiplicative Berger-sphere modulus λ gives the exponential approach, and the S³ Kaluza-Klein kinetic term fixes the coefficient c = √2/3. Slow-roll evaluation gives n_s ≈ 0.967 and tensor-to-scalar ratio r ≈ 0.003, independent of β at leading order — reproducing the Starobinsky predictions without assuming the Starobinsky form, and consistent with Planck 2018 and BICEP/Keck 2021. At subleading order the O(3) exponent yields r = 0.0048, n_s = 0.9578, and running dn_s/dln k = -9.25× 10⁻⁴, all discriminable by CMB-S4. Reheating proceeds via Kibble-Zurek soliton nucleation, non-Gaussianity is small (f_NL ≈ -0.014), and the compact target space provides a natural UV completion.